Certainly! To find the width [tex]\( w \)[/tex] of the base of a rectangular prism when the volume [tex]\( V \)[/tex], the length of the base [tex]\( l \)[/tex] (given as [tex]\( I \)[/tex] in your notation), and the height [tex]\( h \)[/tex] of the prism are known, we will start with the formula for the volume of a rectangular prism:
[tex]\[ V = l \cdot w \cdot h \][/tex]
Given that we know [tex]\( V \)[/tex], [tex]\( l \)[/tex], and [tex]\( h \)[/tex], we want to solve for [tex]\( w \)[/tex]. Let's rearrange the equation to solve for [tex]\( w \)[/tex]:
1. Start with the original formula:
[tex]\[ V = l \cdot w \cdot h \][/tex]
2. To isolate [tex]\( w \)[/tex], divide both sides by [tex]\( l \cdot h \)[/tex]:
[tex]\[ \frac{V}{l \cdot h} = w \][/tex]
Therefore, the width [tex]\( w \)[/tex] of the base of the prism can be calculated using the formula:
[tex]\[ w = \frac{V}{l \cdot h} \][/tex]
Make sure to substitute the given values of [tex]\( V \)[/tex], [tex]\( l \)[/tex], and [tex]\( h \)[/tex] into the equation to find the width [tex]\( w \)[/tex].
So the correct answer is:
[tex]\[ w = \frac{V}{l \cdot h} \][/tex]
